NumericalVGLikelihood.cpp

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/*
 * Copyright (c) The Shogun Machine Learning Toolbox
 * Written (w) 2014 Wu Lin
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice, this
 *    list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * The views and conclusions contained in the software and documentation are those
 * of the authors and should not be interpreted as representing official policies,
 * either expressed or implied, of the Shogun Development Team.
 *
 * Code adapted from
 * and Gaussian Process Machine Learning Toolbox
 * http://www.gaussianprocess.org/gpml/code/matlab/doc/
 *
 * and the reference paper is
 * Nickisch, Hannes, and Carl Edward Rasmussen.
 * "Approximations for Binary Gaussian Process Classification."
 * Journal of Machine Learning Research 9.10 (2008).
 *
 * This code specifically adapted from function in infKL.m
 */

#include <shogun/machine/gp/NumericalVGLikelihood.h>

#ifdef HAVE_EIGEN3
#include <shogun/mathematics/eigen3.h>
#include <shogun/lib/SGVector.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/mathematics/Integration.h>

using namespace Eigen;

namespace shogun
{

CNumericalVGLikelihood::CNumericalVGLikelihood()
    : CVariationalGaussianLikelihood()
{
    init();
}

CNumericalVGLikelihood::~CNumericalVGLikelihood()
{
}

void CNumericalVGLikelihood::init()
{
    SG_ADD(&m_log_lam, "log_lam",
        "The result of used for computing variational expection\n",
        MS_NOT_AVAILABLE);

    SG_ADD(&m_xgh, "xgh",
        "Gaussian-Hermite quadrature base points (abscissas)\n",
        MS_NOT_AVAILABLE);

    SG_ADD(&m_wgh, "wgh",
        "Gaussian-Hermite quadrature weight factors\n",
        MS_NOT_AVAILABLE);

    SG_ADD(&m_GHQ_N, "GHQ_N",
        "The number of Gaussian-Hermite quadrature point\n",
        MS_NOT_AVAILABLE);

    SG_ADD(&m_is_init_GHQ, "is_init_GHQ",
        "Whether Gaussian-Hermite quadrature points are initialized or not\n",
        MS_NOT_AVAILABLE);
    m_GHQ_N=20;
    m_is_init_GHQ=false;

}

void CNumericalVGLikelihood::set_GHQ_number(index_t n)
{
    REQUIRE(n>0, "The number (%d) of Gaussian Hermite point should be positive\n",n);
    if (m_GHQ_N!=n)
    {
        m_GHQ_N=n;
        m_is_init_GHQ=false;
    }
}

SGVector<float64_t> CNumericalVGLikelihood::get_first_derivative_wrt_hyperparameter(
    const TParameter* param) const
{
    REQUIRE(param, "Param is required (param should not be NULL)\n");
    REQUIRE(param->m_name, "Param name is required (param->m_name should not be NULL)\n");
    if (!(strcmp(param->m_name, "mu") && strcmp(param->m_name, "sigma2")))
        return SGVector<float64_t> ();

    SGVector<float64_t> res(m_lab.vlen);
    res.zero();
    Map<VectorXd> eigen_res(res.vector, res.vlen);

    //ll  = ll  + w(i)*lp;
    CLabels* lab=NULL;

    if (supports_binary())
        lab=new CBinaryLabels(m_lab);
    else if (supports_regression())
        lab=new CRegressionLabels(m_lab);

    for (index_t cidx = 0; cidx < m_log_lam.num_cols; cidx++)
    {
        SGVector<float64_t> tmp(m_log_lam.get_column_vector(cidx), m_log_lam.num_rows, false);
        SGVector<float64_t> lp=get_first_derivative(lab, tmp, param);
        Map<VectorXd> eigen_lp(lp.vector, lp.vlen);
        eigen_res+=eigen_lp*m_wgh[cidx];
    }

    SG_UNREF(lab);

    return res;
}

SGVector<float64_t> CNumericalVGLikelihood::get_variational_expection()
{
    SGVector<float64_t> res(m_lab.vlen);
    res.zero();
    Map<VectorXd> eigen_res(res.vector, res.vlen);

    //ll  = ll  + w(i)*lp;
    CLabels* lab=NULL;

    if (supports_binary())
        lab=new CBinaryLabels(m_lab);
    else if (supports_regression())
        lab=new CRegressionLabels(m_lab);

    for (index_t cidx = 0; cidx < m_log_lam.num_cols; cidx++)
    {
        SGVector<float64_t> tmp(m_log_lam.get_column_vector(cidx), m_log_lam.num_rows, false);
        SGVector<float64_t> lp=get_log_probability_f(lab, tmp);
        Map<VectorXd> eigen_lp(lp.vector, lp.vlen);
        eigen_res+=eigen_lp*m_wgh[cidx];
    }

    SG_UNREF(lab);

    return res;
}

SGVector<float64_t> CNumericalVGLikelihood::get_variational_first_derivative(
        const TParameter* param) const
{
    //based on the likKL(v, lik, varargin) function in infKL.m

    //compute gradient using numerical integration
    REQUIRE(param, "Param is required (param should not be NULL)\n");
    REQUIRE(param->m_name, "Param name is required (param->m_name should not be NULL)\n");
    //We take the derivative wrt to param. Only mu or sigma2 can be the param
    REQUIRE(!(strcmp(param->m_name, "mu") && strcmp(param->m_name, "sigma2")),
        "Can't compute derivative of the variational expection ",
        "of log LogitLikelihood using numerical integration ",
        "wrt %s.%s parameter. The function only accepts mu and sigma2 as parameter\n",
        get_name(), param->m_name);

    SGVector<float64_t> res(m_mu.vlen);
    res.zero();
    Map<VectorXd> eigen_res(res.vector, res.vlen);

    Map<VectorXd> eigen_v(m_s2.vector, m_s2.vlen);

    CLabels* lab=NULL;

    if (supports_binary())
        lab=new CBinaryLabels(m_lab);
    else if (supports_regression())
        lab=new CRegressionLabels(m_lab);

    if (strcmp(param->m_name, "mu")==0)
    {
        //Compute the derivative wrt mu

        //df  = df  + w(i)*(dlp);
        for (index_t cidx=0; cidx<m_log_lam.num_cols; cidx++)
        {
            SGVector<float64_t> tmp(m_log_lam.get_column_vector(cidx), m_log_lam.num_rows, false);
            SGVector<float64_t> dlp=get_log_probability_derivative_f(lab, tmp, 1);
            Map<VectorXd> eigen_dlp(dlp.vector, dlp.vlen);
            eigen_res+=eigen_dlp*m_wgh[cidx];
        }
    }
    else
    {
        //Compute the derivative wrt sigma2

        //ai = t(i)./(2*sv+eps); dvi = dlp.*ai; dv = dv + w(i)*dvi;
        VectorXd eigen_sv=eigen_v.array().sqrt().matrix();
        const float64_t EPS=2.2204e-16;

        for (index_t cidx=0; cidx<m_log_lam.num_cols; cidx++)
        {
            SGVector<float64_t> tmp(m_log_lam.get_column_vector(cidx), m_log_lam.num_rows, false);
            SGVector<float64_t> dlp=get_log_probability_derivative_f(lab, tmp, 1);
            Map<VectorXd> eigen_dlp(dlp.vector, dlp.vlen);
            eigen_res+=((m_wgh[cidx]*0.5*m_xgh[cidx])*eigen_dlp.array()/(eigen_sv.array()+EPS)).matrix();
        }
    }

    SG_UNREF(lab);

    return res;
}


bool CNumericalVGLikelihood::set_variational_distribution(SGVector<float64_t> mu,
    SGVector<float64_t> s2, const CLabels* lab)
{
    bool status = true;
    status = CVariationalGaussianLikelihood::set_variational_distribution(mu, s2, lab);

    if (status)
    {
        if (supports_binary())
        {
            REQUIRE(lab->get_label_type()==LT_BINARY,
                "Labels must be type of CBinaryLabels\n");
        }
        else
        {
            if (supports_regression())
            {
                REQUIRE(lab->get_label_type()==LT_REGRESSION,
                    "Labels must be type of CRegressionLabels\n");
            }
            else
                SG_ERROR("Unsupported Label type\n");
        }

        if (supports_binary())
            m_lab=((CBinaryLabels*)lab)->get_labels();
        else
            m_lab=((CRegressionLabels*)lab)->get_labels();

        if (!m_is_init_GHQ)
        {
            m_xgh=SGVector<float64_t>(m_GHQ_N);
            m_wgh=SGVector<float64_t>(m_GHQ_N);
            CIntegration::generate_gauher(m_xgh, m_wgh);
            m_is_init_GHQ=true;
        }

        precompute();

    }

    return status;
}

void CNumericalVGLikelihood::precompute()
{
    //samples-by-abscissas
    m_log_lam=SGMatrix<float64_t>(m_s2.vlen, m_xgh.vlen);

    Map<MatrixXd> eigen_log_lam(m_log_lam.matrix, m_log_lam.num_rows, m_log_lam.num_cols);
    Map<VectorXd> eigen_v(m_s2.vector, m_s2.vlen);
    Map<VectorXd> eigen_f(m_mu.vector, m_mu.vlen);
    Map<VectorXd> eigen_t(m_xgh.vector, m_xgh.vlen);

    VectorXd eigen_sv=eigen_v.array().sqrt().matrix();
    //varargin{3} = f + sv*t(i);   % coordinate transform of the quadrature points
    eigen_log_lam = (
        (eigen_t.replicate(1, eigen_v.rows()).array().transpose().colwise()
         *eigen_sv.array()).colwise()+eigen_f.array()
        ).matrix();
}

} /* namespace shogun */

#endif /* HAVE_EIGEN3 */